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Table 1 Summary of notations and abbreviations used in this study

From: Evolution of nuptial gifts and its coevolutionary dynamics with male-like persistence traits of females for multiple mating

Symbol

Definition and designated values

Model parameters

 v1, v2

Genotypic values of male seminal gift size from male and female parents, respectively. Initial values were given as a normal distribution (mean ± SD = 20 ± 40) with truncation (≥ 20)

 V

Phenotypic value of male seminal gift size, calculated as (v1 + v2)/2

 Vlast

Seminal volume of the last mating of a focal male (Eq. 5)

 m1, m2

Genotypic values of female acceptable number of matings from male and female parents, respectively. Initial values were given as a normal distribution (mean ± SD = 0.5 ± 2) with truncation (≥ 0)

 M

Phenotypic value of female acceptable number of additional matings (= propensity for multiple mating), calculated as (m1 + m2)/2

 MR

Realized number of matings by females

 MO

Optimal number of matings by females, given by solving Eq. 2 with the mean V

 2s

Dominant gene for producing twin slots for receiving gifts

 1s

Recessive gene for producing a single slot for receiving gifts

 2S

Females of the genotype 2s/2s or 2s/1s, having twin slots for receiving gifts

 1S

Females of the genotype 1s/1s, having a single slot for receiving gifts

 R

Mean total volume of resource for producing seminal gifts, ranged from 400 (oligotrophic) to 1300 (eutrophic) by an increment of 100. Each male has a resource budget extracted from a truncated normal distribution mean ± SD = R ± 0.2R (> 0)

 N

Possible number of matings for a focal male, given as R/V, rounded up to the nearest integer

 n

Realized number of matings for a focal male

 r

Cumulative volume of gifts received by a female

 b

Fertilization efficiency (Eq. 1; Fig. 1), given as a constant (b = 0.002)

 c

Female mating cost (per mating), ranged from 5 to 95 by an increment of 10 (Eq. 2)

 FF_max

Maximum female reproductive output (Eq. 1), given as a constant (FF_max = 800)

 FF_pot(r)

Maximum fecundity of a female, as a function of b, FF_max and r, before reduction by mating costs (Eq. 1)

 FF(r, c, MR)

Realized fecundity (= expected fitness) of a female, as a function of b, FF_max, r, MR, and c (Eq. 2)

 P

Paternity share of a male in the offspring of a female mate

 FM(V)

Expected fitness of a male defined by Eq. 3

Paternity determination regimes

 FR

Paternity is determined by fair raffle with respect to the relative gift size received by a focal female

 ES

Paternity is equally shared by all male mates

 LM

The last male monopolizes paternity

 FM

The first male monopolizes paternity

Simulation modes

 CON

Control simulation runs with neither invasion of 2S females nor doubling of female number

 DS

One 2S female per generation was introduced from the1000th generation and beyond

 DF

Number of females were doubled at the 1000th generation and beyond (i.e., 1000 females for 500 males)